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In a long capillary tube of glass, water rises to a height of 4 cm. If the cross-sectional area of the tube were half, the water would have risen to a height of

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$4 \sqrt{2} cm$

$8 cm$

$2 \sqrt{2} cm$

$4 cm$

answer is B.

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Detailed Solution

$h α \frac{1}{r} \Rightarrow h α \frac{1}{{(A)}^{1 / 2}}$

$\frac{h_{1}}{h_{2}} = {(\frac{A_{2}}{A_{1}})}^{1 / 2} = {(\frac{A_{2}}{A})}^{1 / 2}$

$\frac{4}{h_{2}} = \frac{1}{\sqrt{2}}$

$∴ h_{2} = 4 \sqrt{2} c m$

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